A while back I talked about mathematics and how it can be used in fiction. The idea was that there’s more to math fiction than putting in formulas and just generally having the *presence* of mathematics in a story. Mathematics as a field can work in fiction by being used creatively in your worldbuilding while still adhering to its own rules. Maybe it could be used as a form of magic system where performing the magic is like solving a problem. Maybe it plays an important role with your characters and your society, like in Flatland. There’s plenty of ways to look at this. You could even toy with the idea that mathematics doesn’t make sense in your world a la Lewis Carroll. After all, what if the rules of our world become meaningless in yours?

But I said that there’s more to mathematics like there is more to science fiction, and that got me thinking. The two types of sci-fi, hard science fiction and soft science fiction, encompass pretty much everything we know about science fiction today, so where does mathematics come in since that’s basically a science? If mathematics was used in a fictional story, would it have to be like hard science fiction, based only on proven methods and rules?

Here’s some things to keep in mind.

**What Is Hard Science Fiction?**

Hard science fiction follows the rules of science as it pertains to our reality. Basically, the science created for your world is something that would be scientifically possible in our world. Hard science fiction is based on scientific principles, even if some of the things people can do in your society hasn’t been discovered yet in ours. For example, you might come up with a way for teleportation to work in your story that sounds scientifically accurate on paper, even if it’s not possible in real life.

Looking for more information? Check out these examples here.

**So Is Mathematics the Same Thing?**

Yes and No….

Mathematics seems to appear the same way. On the one hand, mathematics can be used in fiction in a creative way, used to create new inventions and systems in a creative work that sounds scientifically accurate on paper. On the other, it’s possible to bend mathematical rules and have everything make sense within a certain fictional context (think, once again, Lewis Carroll’s Alice books). So in the end, math can be manipulated in a creative way while following its rules like how hard science fiction follows the rules of real science and demonstrate a creative output. The big difference involves how mathematics is capable of breaking its rules.

**A Big Difference **

With so many abstract concepts in mathematics, it’s easier to at least bend the rules and have things still make sense. With hard sci-fi, the whole point is that everything is scientifically accurate, even in a basic sense. And the thing with science in general is that, once a scientific idea is proven, looking for different results doesn’t add up to something that physically works. Theories and laws can’t exactly be manipulated. Some types of mathematics can’t be manipulated either. Key word *some*. While parts of mathematics such as formulas and equations can’t be changed in how they work, the abstract ideas of mathematics such as proofs and theorems allow for new ideas to be explored in your world. This almost works in a soft science fiction sense, where something uses science, but it doesn’t follow any scientific principles.

So in the end, mathematical fiction can follow the same methods as writing hard science fiction, but it can go beyond that as well. It can go into soft science fiction territory, it can bend its own rules, or it could just not make sense at all if that’s how your world works. Get creative with it. Just remember that worldbuilding needs to make sense, but more on that later.

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